evaluation of a micropile laterally loaded using

EVALUATION OF A MICROPILE LATERALLY LOADED USING SEMIEMPIRICAL, ANALYTICAL AND

COMPUTATIONAL MODELS FOR GEOTECHNICAL ENGINEERING PRACTICE

CASE OF STUDY: SABANETA

LUIS VILLEGAS NEGRETTE

Dissertation submitted as partial fulfillment of the requirements for the degree of Master in

Engineering

SUPERVISOR: JORGE ALONSO PRIETO SALAZAR

MEDELLÍN

EAFIT UNIVERSITY

SCHOOL OF ENGINEERING

2017

2

Acceptance note

_______________________

_______________________

Chairman

_______________________

Examinator

_______________________

Examinator

_______________________

Medellín

01/12/2017

4

ACKNOWLEDGMENTS

First, I would like to express my gratitude and admiration to my bosses Pedro Salvá and Bernardo

Vieco, thanks for allowing me to use the information consigned on this document for the

development of this research. Their valuable advice and accurate guidelines have helped me to

become the professional I am.

I want to thank my advisor Jorge Alonso Prieto for his mentoring and supervision. Without his

comments, this could not be possible.

I deeply want to recognize the labor of the engineers Laura Sierra and Camilo Pérez, thanks to their

commitment with this project, without that, this research could not be conducted.

Thanks to MIDAS Information Technology Co., Ltd. for allowing me to use a full license of its software

MIDAS GTS NX during the development of this research, without its unconditional help and the

support of the MIDAS LA team this could not have been conceivable. I want to highlight the huge

collaboration from Katerine Hincapie and Angel F. Martínez, thank you for your patience and great

attitude.

I would also like to thank my friends and colleagues Alejandro Velásquez, Carellys Vergara and Jaime

A. Mercado for their comments and suggestion about the structure of this document and their

unconditional support during this process.

I would finally like to express my deepest gratitude to both my relatives and friends, who have

always encouraged me.

ABSTRACT

The Aburrá Valley’s demographic increase has risen house offering. To tackle this local issue,

recently the use of micropiles have spread widely, even though this system has proven to be a

reliable alternative foundation to support vertical loads, its capacity to support lateral loads has

always been a concern. Considering this, this research focuses in the evaluation of the behavior of

a type D micropile’s laterally loaded.

Two lateral load tests results are consigned and one of them is compared with results obtained from

conventional methods used in practical engineering for lateral displacements estimation:

semiempirical formulations, P-Y curves and three-dimensional finite element models.

The geotechnical parameters selection implications for the micropiles type D lateral displacement

evaluation using semiempirical methods and P-Y curves are analyzed and briefly discussed. To

recreate the triaxial tests stress-strain curves, some of the most practical constitutive soil models

currently applied are revised. To evaluate the implications of the micropile injection process in the

micropile lateral displacement estimation, a three-dimensional finite element model is used. Some

alternative proposals for evaluation of the elastic behavior of a micropile laterally loaded are

presented. Finally, conclusions are included, and some research topics are suggested.

KEYWORDS:

Micropile.

Lateral load.

Lateral deformation.

Semiempirical method.

P-Y curves.

Constitutive soil models.

VII

RESUMEN

El incremento poblacional en el Valle de Aburrá ha llevado al aumento de la demanda de la vivienda.

Para atender esto y los problemas locales, el uso de micropilotes como sistema de cimentación se

ha extendido en los últimos años, y a pesar de que ha demostrado ser un sistema confiable para

atender cargas verticales, su capacidad para atender solicitaciones horizontales siempre ha

quedado en duda. Por eso, este trabajo se enfoca en la evaluación del comportamiento de un

micropilote tipo D sometido a cargas laterales.

Se presentan los resultados de dos pruebas de carga lateral y uno de ellos se compara con los

métodos convencionales usados en la ingeniería práctica para la estimación de desplazamientos

laterales: formulaciones semiempíricas, curvas P-Y y modelos de elementos finitos en tres

dimensiones.

Las implicaciones de la elección de los parámetros geotécnicos para la evaluación del

comportamiento lateral de micropilotes tipo D usando métodos semiempíricos y curvas P-Y son

analizadas y levemente discutidas. Para recrear las curvas de Esfuerzo-Deformación de los ensayos

triaxiales, se revisaron algunos de los modelos constitutivos más prácticos aplicados en la actualidad.

Uno modelo tridimensional de elementos finitos es usado para evaluar las implicaciones del proceso

de inyección de los micropiles en la estimación del desplazamiento lateral. Se presentan algunas

propuestas alternativas para la evaluación del comportamiento elástico de un micropilote

lateralmente cargado. Finalmente, se dan las conclusiones y recomendaciones para futuras

investigaciones.

PALABRAS CLAVE:

Micropilote.

Carga lateral.

Deformación lateral.

Método semiempírico.

Curvas P-Y.

Modelos constitutivos de suelo.

VIII

TABLE OF CONTENTS

ACKNOWLEDGMENTS ............................................................................................................. 4

ABSTRACT .............................................................................................................................. VI

RESUMEN .............................................................................................................................. VII

TABLE OF CONTENTS ............................................................................................................ VIII

LIST OF FIGURES ......................................................................................................................XI

LIST OF TABLES ..................................................................................................................... XIV

LIST OF ANNEXES .................................................................................................................. XV

LIST OF SYMBOLS ................................................................................................................. XVI

1 INTRODUCTION ............................................................................................................... 1

1.1 OBJECTIVES...................................................................................................................................... 2

1.2 SCOPE OF RESEARCH ....................................................................................................................... 2

2 BACKGROUND ................................................................................................................. 3

2.1 MICROPILES ..................................................................................................................................... 3

2.2 PILES LATERALLY LOADED ................................................................................................................ 7

2.2.1 ULTIMATE LATERAL RESISTANCE ....................................................................................................... 7

2.2.2 THEORY OF ELASTICITY ...................................................................................................................... 8

2.2.3 ELASTIC BEAM FOUNDATION ............................................................................................................ 8

2.2.4 SEMIEMPIRICAL FORMULATIONS ...................................................................................................... 9

IX

2.2.5 NAVFAC METHOD ............................................................................................................................ 12

2.2.6 NONDIMENSIONAL CHARTS ............................................................................................................ 14

2.2.7 P-Y CURVES ...................................................................................................................................... 15

2.2.8 CHARACTERISTIC LOAD METHOD .................................................................................................... 16

2.2.9 COMPUTATIONAL MODELS ............................................................................................................. 16

2.3 MICROPILES LATERALLY LOADED ................................................................................................... 19

3 CASE STUDY ................................................................................................................... 22

3.1 DESCRIPTION ................................................................................................................................. 22

3.2 GEOLOGICAL CHARACTERISTICS .................................................................................................... 23

3.2.1 MIGMATITAS DE PUENTE PELÁEZ (TRMPP) ..................................................................................... 23

3.2.2 DEPÓSITOS DE FLUJO DE LODOS Y/O ESCOMBROS (NQFII) ............................................................ 24

3.3 GEOTECHNICAL CHARACTERISTICS ................................................................................................ 24

3.3.1 SURVEY RESULTS .............................................................................................................................. 25

3.4 MICROPILES LOAD TESTS ............................................................................................................... 32

3.4.1 VERTICAL LOAD TEST ....................................................................................................................... 35

3.4.2 LATERAL LOAD TEST ......................................................................................................................... 36

4 ANALYSES....................................................................................................................... 38

4.1 CURRENT PRACTICAL USED MODELS ............................................................................................. 38

4.2 MODELING .................................................................................................................................... 38

4.2.1 BEAM ON ELASTIC FOUNDATION USING SEMIEMPIRICAL FORMULATIONS ................................... 39

4.2.2 P-Y CURVES ...................................................................................................................................... 44

4.2.3 COMPUTATIONAL MODEL ............................................................................................................... 48

5 ADDITIONAL APPROACH ................................................................................................ 58

6 CONCLUSIONS AND RECOMMENDATIONS .................................................................... 63

X

6.1 CONCLUSIONS ............................................................................................................................... 63

6.2 RECOMMENDATIONS .................................................................................................................... 64

7 REFERENCES .................................................................................................................. 66

8 ANNEXES ........................................................................................................................ 66

XI

LIST OF FIGURES

Fig. 1. Micropile classification system, a) Application classification Case 1, b) Application

classification Case 2 and c) Types of grouting. After (FHWA 2005). ...................................................3

Fig. 2. Scheme of a hollow bar micropile. Adapted from (Abd El-aziz 2012). .....................................5

Fig. 3. Rotation required to mobilize active and passive earth resistance. After (Budhu 2015). .......7

Fig. 4. Coefficient of variation of subgrade reaction. After (NAVFAC 1986). ................................... 13

Fig. 5. Coefficients for long piles in cohesive soils. Adapted from (Das 2002). ............................... 15

Fig. 6. Project location. After Google Earth 2016. ........................................................................... 22

Fig. 7. Regional geology. After (A.M.V.A 2007). ............................................................................... 23

Fig. 8. Geotechnical survey location on the original terrain conditions. .......................................... 24

Fig. 9. Location of field tests and micropiles vertically and horizontally tested. .............................. 26

Fig. 10. Summary of basic characterization laboratory tests. ........................................................... 27

Fig. 11. Summary of field tests and mechanical soil resistance based on some laboratory tests. ... 28

Fig. 12. Summary of soil parameters. ............................................................................................... 29

Fig. 13. NQfll's boulder. ..................................................................................................................... 30

Fig. 14. Res. V and Res. V (2) materials. ............................................................................................ 31

Fig. 15. Site conditions and micropile's reinforcement. ................................................................... 33

Fig. 16. Exhumed micropiles. ............................................................................................................ 34

Fig. 17. Vertical load test - M-PC-V. .................................................................................................. 35

Fig. 18. Lateral Load tests. a) M1-PC-H and b) M2-PC-H results. ..................................................... 37

XII

Fig. 19. SAP 2000 model. a) Micropile cross section, and b) 3D model. .......................................... 41

Fig. 20. Comparison between lateral load test result against lateral response of a beam on elastic

foundation using semiempirical methodologies for: a) the lowest soil’s parameters, b) average

soil’s parameters, and c) the highest soil’s parameters. .................................................................. 43

Fig. 21. ALLPILE Model. a) micropile characteristics, b) the lowest soil’s parameters, c) average

soil’s parameters, and d) the highest soil’s parameters. .................................................................. 44

Fig. 22. P-Y curves for: a) the lowest soil’s parameters, b) average soil’s parameters, and c) the

highest soil’s parameters. ................................................................................................................. 45

Fig. 23. Comparison between lateral load test result against lateral response of a beam on elastic

foundation using P-Y curves method for: a) the lowest soil’s parameters, b) average soil’s

parameters, and c) the highest soil’s parameters. ........................................................................... 47

Fig. 24. NQfll constitutive model evaluation. a) Mohr Coulomb model, b) Duncan-Chang model

and c) Hardening Soil model. ............................................................................................................ 49

Fig. 25. 3D model. a) soil layer and b) micropile element. .............................................................. 51

Fig. 26. Micropile characteristics. a) equivalent material properties and b) cross section. ............ 51

Fig. 27. Lateral displacement evaluation at: a) micropile's head and b) along micropile's depth. .. 53

Fig. 28. Lateral displacement evaluation with NQfll’s reference modulus and OCR scaled. a)

micropile's head and b) along micropile's depth. ............................................................................. 55

Fig. 29. Lateral displacement evaluation with NQfll Mohr Coulomb model using soil’s modulus

after injection. a) micropile's head and b) along micropile's depth. ............................................... 56

Fig. 30. Soil shear stress conditions during a lateral load test. ......................................................... 59

Fig. 31. Evaluation of M1-PC-H lateral load test result again proposed formulation for the elastic

part. ................................................................................................................................................... 60

XIII

Fig. 32. Evaluation of M2-PC-H lateral load test result compared to proposed formulation for the

elastic part and affected by (Mezazigh 1995). .................................................................................. 61

XIV

LIST OF TABLES

Table 1. A values. After (Terzaghi 1955). .............................................................................................9

Table 2. Values of 𝑘𝑠1 in kPa for square plates 30 cm x 30 cm and for long strips, 30 cm wide,

resting on pre-compressed clay. Adapted from (Terzaghi 1955). ................................................... 10

Table 3. 𝑘ℎ semiempircal formulations. ........................................................................................... 10

Table 4. Numerical values of m coefficient. After (Broms 1964a). .................................................. 11

Table 5. Estimated values for 𝑘ℎ. Adapted from (Davisson 1970). ................................................. 11

Table 6. 𝑛ℎ and 𝑘ℎ values. Adapted from (Robinson 1979). ........................................................... 12

Table 7. Coefficients for long piles in granular soils. Adapted from (Das 2002). .............................. 14

Table 8. Overview of model parameters and selection methods. Adapted from (Brinkgreve 2005).

.......................................................................................................................................................... 18

Table 9. Basic Index and soil’s resistance parameters. ..................................................................... 31

Table 10. NQfll layer moduli of subgrade reaction - semiempirical formulations - Lowest case. .... 39

Table 11. NQfll layer moduli of subgrade reaction - semiempirical formulations - Intermediate

case. .................................................................................................................................................. 39

Table 12. NQfll layer moduli of subgrade reaction - semiempirical formulations - Highest case. ... 40

Table 13. Constitutive soil parameters for each soil layer modeled with HS. .................................. 50

Table 14. Constitutive soil parameters for each soil layer modeled with MC. ................................. 50

Table 15. Evaluation of equations (2) to (4). .................................................................................... 54

Table 16. Moduli of subgrade reaction using proposed formulation for springs each meter along

micropile element. ............................................................................................................................ 60

XV

Table 17. Evaluation of coefficients of reduction due to slope proximity using (Mezazigh 1995). .. 60

Table 18. Moduli of subgrade reaction using proposed formulation and (Mezazigh 1995)

methodology. .................................................................................................................................... 61

LIST OF ANNEXES

Annex 1- Res. V layer moduli of subgrade reaction - semiempirical formulations – Lowest case ... 72

Annex 2. Res. V layer moduli of subgrade reaction - semiempirical formulations -Highest case. ... 72

Annex 3. Res. V (2) layer moduli of subgrade reaction - semiempirical formulations - Lowest case.

.......................................................................................................................................................... 73

Annex 4. Res. V (2) layer moduli of subgrade reaction - semiempirical formulations - Highest case.

.......................................................................................................................................................... 73

Annex 5. Res. IV layer moduli of subgrade reaction - semiempirical formulations - Lowest case. .. 73

Annex 6. Res. IV layer moduli of subgrade reaction - semiempirical formulations - Highest case. . 74

Annex 7. Lateral evaluation using P-Y curves - lowest case.............................................................. 77

Annex 8. Lateral evaluation using P-Y curves - average case. .......................................................... 81

Annex 9. Lateral evaluation using P-Y curves – highest case. ........................................................... 85

Annex 10. Res. V. HS Model calibration. ........................................................................................... 86

Annex 11. Res. V (2). HS Model calibration. ..................................................................................... 86

XVI

LIST OF SYMBOLS

𝑇𝐿 Ultimate traction or compression micropile capacity

𝑞𝑠 Ultimate grout to ground bond strength

Ds Average bond diameter

Ls Bond length

𝐿0 Depth of influence

𝐸𝑝 Micropile’s elasticity modulus

𝐼𝑝 Micropile’s inertia

𝐸𝑠 Soil’s elasticity modulus

𝑃 Reaction intensity

𝑘 Supporting medium stiffness

𝑦 Beam’s deflection

𝑘ℎ Coefficients of horizontal subgrade reaction

𝑧 Depth of analysis below ground surface

𝑑 Pile’s width

𝛾 Effective unit weight

�̅�𝑠1 Basic coefficient of vertical subgrade reaction (for square area with width B = 30 cm)

𝑞𝑢 Unconfined compressive strength

𝐶𝑢, 𝑆𝑢 Undrained shear strength

XVII

φ’ Effective friction angle

𝜈 Poisson’s ratio

𝑒 Void ratio

𝑣𝑠 Shear wave velocities

𝐿 Pile length

𝑚 Coefficient

𝜎′ Vertical effective stress

𝑦𝑢 Ultimate displacement

𝑦𝑧 Lateral displacement

𝜃𝑧 Rotation

𝑁𝑞, 𝑁𝛾 Bearing capacity factors

N Number of blows per foot (30 cm)

y/d Normalized deflection

A, 𝑓, 𝐴𝑥, 𝐵𝑥, 𝐴𝜃, 𝐵𝜃, 𝐴𝑚, 𝐵𝑚, 𝐴𝑣, 𝐵𝑣, 𝐴𝑝′, 𝐵𝑝, 𝐴′𝑦, 𝐵′𝑦, 𝐴′𝑚, 𝐵′𝑚 Coefficients

𝑀 Moment applied at pile head

𝑀𝑧 Internal bending moment

𝑉𝑧 Internal shear force

Pc Characteristic load

Mc Characteristic moment

XVIII

𝑇 Characteristic length of the soil-pile system

τ Shear stress

𝐺 Shear modulus

𝛾 Shear strain

𝐹 Internal shear force

𝐴 Transversal area where shear force is acting

𝜌 Soil density

g Gravity

t Distance between micropile and slope crest

tlim Limit distance

r Reduction coefficient

β Slope angle

1 INTRODUCTION

Over the last decades the Aburrá Valley’s population has grown significantly as it is presented by

(Departamento Administrativo Nacional de Estadística 2017a), as a consequence, construction firms

have been forced to intensify the housing offers and to improve their building practices in order to

be more competitive and increase their income in a shorter period of time as it is inferred from the

results of the (Departamento Administrativo Nacional de Estadística 2017b) buildings census.

To optimize the constructible areas, buildings of the Aburrá Valley are getting higher every day, what

has resulted on a significant increase in service loads coming from the superstructure to the subsoil.

For this reason, the need of a better understanding of subsoil conditions and the improvement of

construction methods has become a constant.

Over the last 5 years, these construction firms have decided to buy micropile drilling rigs to reduce

the direct cost of foundation systems, to avoid outsourcing and to have less time-consuming way to

build foundations.

Even when the acquisition of micropile’s construction equipment has been a profitable investment

for construction firms, the Geotechnical design possibilities have been reduced almost exclusively

to micropiles solutions and the wordiness about the reliability of this foundation system has become

a constant.

Traditionally, micropiles are designed using some methodologies like (Lizzi 1982) and (Bustamante

1985), or design guidelines as (FHWA 2005), (Ministère de l’Équipement des Transports 1993) and

(Dirección General de Carreteras 2005); nevertheless, these methodologies or guidelines are

focused on the design of this element for vertical loads, and its lateral load resistance is lightly

discussed or just neglected.

In concordance with the geological and geomorphological characteristics of the Aburrá Valley and

its medium seismic hazard, most of the buildings of the Valley are constructed on places of moderate

to very high slopes (Área Metropolitana del Valle de Aburrá 2012) and medium seismic risk

(Ministerio de Ambiente Vivienda y Desarrollo Territorial 2010). These imply the presence of

horizontal loads that must be supported by the structure of the building and its foundation system.

2

During a seismic event, deep foundations need to support lateral loads due to the initial lateral

movements of the soil mass and the consequential interaction between foundation elements and

the kinematic forces coming from the superstructure. This has been discussed by several authors

like (Zeevaert 1983) and (Thilakasiri et al. 2009).

For the structural design of laterally loaded foundation elements, commonly, structural designers

replace the soil by elastic equivalent springs. For certain conditions, this simplification can be

considered correct (Day and Mucillo 2014), nevertheless; the reliability of the geotechnical methods

to estimate these springs is the real concern, because there are a lot of methodologies to estimate

them, but rarely the lateral expected behavior is confronted with the real one measured.

Currently, there are several methodologies developed to evaluate the lateral resistance and

displacement of piles built on a specific type of soil and for specific pile conditions, however; these

were not directly established for micropile elements; for which the construction method, small

diameter and high reinforcement area are variables that are not considered on the actual lateral

pile resistance formulation.

1.1 OBJECTIVES

To evaluate some current geotechnical methodologies used for lateral evaluation of deep

foundations, analyzing their applicability to IRS micropiles built on the Aburrá Valley based on

results of an IRS micropile laterally loaded.

- To perform a micropile lateral load test.

- To evaluate semiempirical moduli of subgrade reaction and their reliability.

- To calibrate a practical soil constitutive model to represent soils behavior.

- To simulate micropile lateral load test measurements.

1.2 SCOPE OF RESEARCH

The evaluation of the micropile laterally loaded is just for geotechnical purposes; considering

specific site conditions and a construction method.

3

2 BACKGROUND

2.1 MICROPILES

Micropiles are a type of deep foundation solution conceived by (Lizzi 1950) as a technique for

underpinning historical buildings affected by World War II.

The use of micropiles has extended from its original function. Nowadays, they are used to improve

soils resistance and as foundation solution. Micropiles can be classified according to their use or

construction grouting technique (FHWA 2005). Fig. 1 shows the (FHWA 2005) classification system.

a

c

b

Fig. 1. Micropile classification system, a) Application classification Case 1, b) Application classification Case 2 and c) Types of grouting. After (FHWA 2005).

Case 1 micropiles are used to support vertical and lateral loads from the structure. Moreover, Case 2

micropiles are elements that work as a reticular arrangement to reinforce soil mass and improve its

resistance.

4

The grouting (FHWA 2005) classification system is similar to DTU 13.2 used in France (L’École

Nationale des Ponts et Chaussées 2004). The association and description of each classification

system is shown below.

• Type A or II: foundation elements grouted by a sand-cement mortar or cement grout; placed

by gravity head and non-injected.

• Type B or I: micropile’s neat cement grout is placed into a pre-bored hole using injection

pressure lower than in-situ lateral soil pressure to avoid hydrofracturing of surrounding soil.

Typically, this injection pressure is lower than 1 MPa.

• Type C or III: is a two-stage procedure, the first stage, a micropile Type A is developed. In

the second stage (15 to 25 minutes later), the grouting procedure is repeated applying a

higher lateral injection pressure, which is close to the pressuremeter limit pressure and in

all cases higher than 1 MPa. This kind of injection is worldwide known as IGU (Injection

Globale et Unitaire).

• Type D or IV: as Type C, this methodology is a two-stage procedure. In the first one, a

micropile Type B is constructed, and in the second one (after grouting has hardened),

additional grout is injected using lateral pressures higher than pressuremeter limit pressure;

commonly this pressure ranges between 2 to 8 MPa. This procedure can be performed

several times as it is required and it is commonly known as IRS (Injection Répétitive et

Sélective).

Another type of micropile that exists but is not classified yet, consists of a hollow steel bar that is

employed as drilling rod during its installation and at the same time as a conduit for delivering the

flushing fluid under pressure through the lost bit holes that is mounted on the tip of the bar, which

allows the grouting to flush from the bottom of the borehole while drill is performed. This kind of

micropile is commonly categorized as a Type B micropile, nevertheless; its construction procedure

is totally different, for this reason some authors (Abd El-aziz 2012) have proposed to classify this

micropile as Type E. In Fig. 2 a scheme of a Type E micropile is presented.

5

Fig. 2. Scheme of a hollow bar micropile. Adapted from (Abd El-aziz 2012).

Generally, a micropile is also characterized by its small diameter (less than 300 mm), slender ratios

greater than 100 (L’École Nationale des Ponts et Chaussées 2004) and its mechanism of resistance.

Micropiles are usually designed to support vertical loads by considering only their lateral resistance

capacity and neglecting their point capacity. The typical formulation used for the geotechnical

design of these elements is shown on (1).

𝑇𝐿 = qs π D𝑠 Ls (1) where, 𝑇𝐿 is the ultimate traction or compression capacity, 𝑞𝑠 is the ultimate grout to ground bond strength, Ds is the average bond diameter, and Lsis the bond length.

Some practical values and formulations i.e. (Bustamante 1985; Dirección General de Carreteras

2005; FHWA 2005) have been used to evaluate 𝑞𝑠. Nevertheless, this parameter is not just function

of a specific soil type, installation grouting techniques used on its construction method are

6

important too. Taking into a count all these variables, load testing probes are commonly required

to verify design assumptions.

On the other hand, for (FHWA 2005) one of the greatest limitations of micropiles is their lateral

capacity. Sometimes, the main concern is just the vertical load, however, this conception is a

mistake, particularly during a seismic event, where kinematic forces will result in a considerable

lateral force requirement for the foundation system. As it is pointed out by (Richards and Rothbauer

2004), lateral load case often governs the design of micropiles and not just the vertical case.

Currently, lateral capacity of micropiles is estimated using theories developed for pile foundations,

which do not consider the effect of the small diameter, the reinforcement controlling function and

the installation method.

Sometimes, micropiles work as a group because they are connected by a cap to guarantee their

unity. When a lateral solicitation exists, it is common to use a passive earth pressure resistance

acting on the lateral side of the cap to verify its stability. Nevertheless, the ratio of displacement

needed to develop a passive earth pressure on the cap can be excessive when it is compared to the

elastic lateral displacement capacity of a micropile. Thus, a plastic hinge will be produced at certain

depth. Consequently, micropiles will not be able to support the service loads coming from the

superstructure.

To evaluate the influence of the lateral load on the micropile element, some formulations have been

proposed. Equations (2) to (4) are some of the most used.

Author Equation (FHWA 2005) 𝐿0 = 20Ds (2) (Richards and Rothbauer 2004) 𝐿0 = 2 to 5 m (3)

(L’École Nationale des Ponts et Chaussées 2004) 𝐿0 = √4𝐸𝑝𝐼𝑝

𝐸𝑠

4

(4)

where, 𝐿0 is the depth of influence, 𝐸𝑝 is the micropile’s elasticity modulus, 𝐼𝑝 is the micropile’s

inertia, and 𝐸𝑠 is the soil modulus of elasticity

Generally, when groups of micropiles are used as foundation system lateral loads are supported by

adding some battered micropiles at the cap. Nevertheless, (FHWA 2005) do not recommend this

solution when ground will potentially settle around.

7

2.2 PILES LATERALLY LOADED

The evaluation of a pile laterally loaded can be performed based on its ultimate lateral resistance

or by its allowable lateral displacement.

2.2.1 ULTIMATE LATERAL RESISTANCE

Some of the most common methodologies used to evaluate ultimate lateral resistance of soil were

proposed by authors like (Brinch-Hansen 1961) and (Broms 1964a; b).

Brinch Hansen method assumes that the pile is rigid and no yield hinge can be developed, so the

pile rotates as a rigid body at a certain point below the ground surface.

The above-mentioned assumptions consider that Rankine’s passive earth pressure will be developed

in front of the pile, and at the same time, behind the pile the active earth pressure will take place.

To develop passive earth pressure, lateral displacements are needed to be allowed, this

displacement can be as large as a value close to 10% of a cantilever (pile’s length), as it is shown on

Fig. 3, where is presented the displacement needed to reach an earth pressure of a specific type of

soil as a function of cantilever’s height.

Fig. 3. Rotation required to mobilize active and passive earth resistance. After (Budhu 2015).

8

Brinch Hansen methodology can be used to estimate the ultimate lateral resistance of a pile-soil

system, however, this method is not able to evaluate lateral displacements as is noted by (Ruigrok

2010).

Alternatively, Broms’ formulation can be used to compute lateral deflections, ultimate lateral

resistance and maximum bending moments for free head or restricted driven piles into saturated

cohesive and cohesionless soils.

Broms proposed his formulation based on elastic theory to determine the behavior of pile element

and soil’s support reaction, he also considered that failure happens when pile’s section ultimate

stress or supporting soil ultimate stress is achieved.

To estimate the ultimate lateral resistance of soil, the author assumed that when a long pile is used

a plastic hinge will take place at a certain depth, and that above it, the full passive resistance of soil

will be developed.

Broms’ method was established based on available lateral load test results, which at his time were

limited, this is the reason why he recommended using his methodology with caution.

2.2.2 THEORY OF ELASTICITY

This theory expresses the elastic stress-strain relationship of a material based on Hooke’s law as it

is mentioned by (Timoshenko and Goodier 1951).

2.2.3 ELASTIC BEAM FOUNDATION

According to (Hetényi 1946) the elastic beam foundation methodology is based on (Winkler 1867)

and (Zimmermann 1888) works. For this formulation, a perpendicular load is assumed to act along

a beam member, the cross section is uniform and the element is supported by an elastic medium

which will deflect as response of the applied load; therefore, a distributed reaction force will be

produced on the supporting medium. The following equation was proposed to represent this

behavior.

9

𝑃 = 𝑘 𝑦 (5) Where, 𝑃 is the reaction intensity, 𝑘 is the supporting medium stiffness, and 𝑦 is the beam’s deflection.

Equation (5) involves that reacting medium is elastic; its constitutive material follows Hooke’s law

and 𝑘 is a constant of proportionality that is just valid for the specific point of evaluation.

Using the elastic beam foundation formulation, a discretization of the element loaded, the flexural

stiffness of a beam, equilibrium equations and differential procedures, is then possible to partially

formulate equations to determine the internal forces of elements perpendicularly loaded. However,

it is not possible to solve it directly and it will require the use of boundary conditions evaluations to

find some integration constants. A detailed discussion of these formulations can be found on

(Hetényi 1946).

2.2.4 SEMIEMPIRICAL FORMULATIONS

Several authors had formulated semiempirical coefficients of horizontal subgrade reaction (𝑘ℎ )

based on the elasticity theory and pile lateral load test literature reported or developed by them.

One of the first authors who proposed a semiempirical formulation was (Terzaghi 1955). He

developed independent formulations for sands and clays.

For sands, he considered that 𝑘ℎ depends on the depth of analysis below ground surface (𝑧), pile’s

width measured at right angles to the direction of projected lateral displacement (𝑑), the effective

unit weight (𝛾) and relative density of sand. As a result, the following formulation was proposed.

𝑘ℎ =𝐴 𝛾 𝑧

1.35 𝑑

(6)

where, A is a coefficient, see Table 1.

Table 1. A values. After (Terzaghi 1955).

Relative density of sand Loose Medium Dense

Range of values of A 100-300 300-1000 1000-2000

Adopted values of A 200 600 1500

10

Another form to present (6) is substituting 𝐴 𝛾

1.35 value by 𝑛ℎ, what results in (7).

𝑘ℎ = 𝑛ℎ

𝑧

𝑑 (7)

For piles embedded in stiff clays, the 𝑘ℎ value is supposed to be constant with depth and is just

function of pile’s width. According to (Terzaghi 1955) this value can be estimated using (8).

𝑘ℎ =�̅�𝑠1

1.5 𝑑

(8)

where, �̅�𝑠1 is the basic value of coefficient of vertical subgrade reaction (for square area with width B = 30 cm).

Suggested values proposed by (Terzaghi 1955), are shown on Table 2.

Table 2. Values of �̅�𝑠1 in kPa for square plates 30 cm x 30 cm and for long strips, 30 cm wide, resting on pre-compressed clay. Adapted from (Terzaghi 1955).

Consistency of clay Stiff Very stiff Hard

Values of 𝑞𝑢 (kPa) 95 – 191.5 191.5 - 383 > 383

Range for �̅�𝑠1, square plates 50 - 100 100 – 200 > 200

Proposed values, square plates 75 150 300

Various authors have used the same Terzaghi’s formulation and have derivated 𝑛ℎ and 𝑘ℎ values

for specific conditions. Some of the most common used on engineering practice are presented on

the following table.

Table 3. 𝑘ℎ semiempircal formulations.

Formulation Equation

(Vesic 1961) 𝑘ℎ =0.65 𝐸𝑠

𝑑(1 − 𝜈2)√

𝐸𝑠𝑑4

𝐸𝑝𝐼𝑝

12

(9)

(Francis 1964) 𝑘ℎ = 1885.08𝛾𝑑𝑁𝛾 + 3770.16𝛾𝑧𝑁𝑞 (10)

(Broms 1964a) 𝑘ℎ =

𝐸𝑠

𝑚 (1 − 𝜈2)√𝐿 𝑑

(11)

𝑚 values are shown on Table 4

(Pise 1977) 𝑘ℎ = 𝑛ℎ𝑧23 (12)

(Audibert and Nyman 1977)

𝑘ℎ =1

𝐴 + 𝐵𝑦

(13) 𝐴 =

0.145 𝑦𝑢

𝑦𝑍𝑁𝑞 𝐵 =

0.855

𝑦𝑍𝑁𝑞

11

(Kishida and Nakai 1977)

𝑘ℎ =1.3 𝐸𝑠

𝑑(1 − 𝜈2)√

𝐸𝑠𝑑4

𝐸𝑝𝐼𝑝

12

(14)

(Robinson 1979)

𝑘ℎ = 67 𝑆𝑢

𝑑 (15)

(Bhushan et al. 1981)

log 𝑙𝑘ℎ = 0.82 + log 𝑁 − 0.62 log𝑦

𝑑 (16)

𝑘ℎ = 271.447 (100.82+ log 𝑁−0.62 log𝑦𝑑) (17a)*

(Sogge 1981) 𝑘ℎ = 314.18 𝑡𝑜 4712.7 𝑧

𝑑 (18)

(Pyke and Beikae 1984)

𝑘ℎ = 2𝐸𝑠

𝑑 (19)

(Habibagahi and Langer 1984)

𝑘ℎ =𝜎′𝑁𝑞

𝑦

(20)

𝑁𝑞 = 𝐴 + √𝑧

𝑑

For 30°, A = 5,9,12 and 15 for y=2.54, 6.35, 12.7

and 25.4 mm

where, 𝐸𝑠 is the soil modulus of elasticity, 𝐸𝑝 is the pile elasticity modulus, 𝐼𝑝 is the pile inertia,

𝜈 is the Poisson’s ratio, 𝐿 is the pile length, 𝑚 is the coefficient, see Table 4, 𝜎′ is the vertical effective stress, 𝑦𝑢 is the ultimate displacement, 𝑁𝑞 and 𝑁𝛾 are the bearing capacity factors, N

is the SPT resistance over the embedded length of pile (blows/ft), y/d is the normalized deflection (%), and 𝑙𝑘ℎ is the coefficient of subgrade reaction (lb/in3). *International System Adapted equation (kPa/m).

Table 4. Numerical values of m coefficient. After (Broms 1964a).

L/d 1.0 1.5 2 3 5 10 100

m 0.95 0.94 0.92 0.88 0.82 0.71 0.37

Even though several authors proposed some mathematical formulations for 𝑘ℎlike those shown on

Table 3, others preferred to use intervals.

(Davisson 1970) suggested some 𝑛ℎ and 𝑘ℎ values based on his personal experience and literature

reported values, see Table 5.

Table 5. Estimated values for 𝑘ℎ. Adapted from (Davisson 1970).

Soil type Value

Granular soils 𝑛ℎ ranges from 1.5 to 200 lb/in3; is relative proportional to relativity density

Normally loaded organic silt

𝑛ℎ ranges from 0.4 to 3 lb/in3

Peat 𝑛ℎ is approximately 0.2 lb/in3

12

Cohesive soils 𝑘ℎ is approximately 67 𝐶𝑢

Based on field test data of lateral load test on timber piles in cohesionless soil, (Robinson 1979)

suggested that 𝑘ℎ is independent from pile’s width, and recommended the use of 𝑘ℎ and 𝑛ℎ values

presented on Table 6.

Table 6. 𝑛ℎ and 𝑘ℎ values. Adapted from (Robinson 1979).

Soil Conditions Horizontal Subgrade Reaction

Soil description N Su,

(kPa) Horizontal movement (mm)

Type Value Compute from Deflection (kPa)

Amorphous peat <1 26.42 𝑘ℎ 689.47

3ft sand 9.52 𝑘ℎ 3447.38

over amorphous peat

𝑘ℎ 689.47

4ft gravelly clay 38.3 7.87 𝑘ℎ 5102.12

over clayey silt 1.5 19.1 𝑘ℎ 2551.06

5ft stiff clay 3 57.4 9.40 𝑘ℎ 3447.38

over silt and peat 1 19.1 𝑘ℎ 2068.43

Organic clay silt <1 14.4 15.24 𝑘ℎ 113.76

Layered silty sand 3 22.86 𝑛ℎ 206.84

and sandy silt

Layered sand and 5 6.35 𝑛ℎ 427.47

sandy silt

3.5ft sand 10 2.79 𝑛ℎ 1765.06

over clayey silt 4

Silty sand 5 6.09 𝑛ℎ 689.47

Slightly organic silt

2 16.26 𝑛ℎ 103.42

3ft organic silt 1 17.27 𝑛ℎ 234.42

over sandy silt 3

It is important to notice that some theories have been originally developed for vertical subgrade

modulus, nevertheless, they are often used to estimate lateral behavior. Some of the most common

used are (M.A.Biot 1937), (Skempton 1951) and (Broms 1964a).

2.2.5 NAVFAC METHOD

(NAVFAC 1986) procedure is based on the modulus of subgrade reaction and the idealized

assumption that lateral loads do not exceed a third of ultimate lateral load capacity. For Granular

13

soils and normally consolidated cohesive soil 𝑘ℎ is assumed to increase linearly with depth, this is

expressed by (21).

𝑘ℎ =𝑓 ∗ 𝑧

𝑑 (21)

where, 𝑓 is the coefficient of variation of lateral subgrade reaction (ton/ft3), see Fig. 4.

Fig. 4. Coefficient of variation of subgrade reaction. After (NAVFAC 1986).

For heavily consolidated cohesive soils the coefficient of lateral subgrade reaction is considered

constant with depth. According to (NAVFAC 1986) the coefficient varies between 35 up to 70 Cu/d.

14

2.2.6 NONDIMENSIONAL CHARTS

This method derives from the differential equation for beam-column on a foundation given by

(Hetényi 1946), the elasticity principles and some fundamental identities. Based on these principles

the following equations can be defined for granular soils.

𝑦𝑧 = 𝐴𝑥

𝑃𝑇3

𝐸𝑝𝐼𝑝+ 𝐵𝑥

𝑀𝑇2

𝐸𝑝𝐼𝑝 (22)

𝜃𝑧 = 𝐴𝜃

𝑃𝑇2

𝐸𝑝𝐼𝑝+ 𝐵𝜃

𝑀𝑇


𝑀𝑧 = 𝐴𝑚𝑃𝑇 + 𝐵𝑚𝑀 (24)

𝑉𝑧 = 𝐴𝑣𝑃 + 𝐵𝑣

𝑀

𝑇 (25)

𝑝′𝑧 = 𝐴𝑝′

𝑄

𝑇+ 𝐵𝑝′

𝑀

𝑇2 (26)

where, 𝐴𝑥, 𝐵𝑥, 𝐴𝜃, 𝐵𝜃, 𝐴𝑚, 𝐵𝑚, 𝐴𝑣, 𝐵𝑣, 𝐴𝑝′, 𝐵𝑝′ are coefficients (see the table), 𝑀 is the

moment applied at pile head (kN*m), and 𝑇 is the characteristic length of the soil-pile system.

𝑇 = √𝐸𝑝𝐼𝑝

𝑛ℎ

5

𝑍 =𝑧

𝑇

Table 7. Coefficients for long piles in granular soils. Adapted from (Das 2002).

Z 𝑨𝒙 𝑨𝜽 𝑨𝒎 𝑨𝒗 𝑨𝒑′ 𝑩𝒙 𝑩𝜽 𝑩𝒎 𝑩𝒗 𝑩𝒗

0.0 2.435 -1.623 0.000 1.000 0.000 1.623 -1.750 1.000 0.000 0.000

0.1 2.273 -1.618 0.100 0.989 -0.227 1.453 -1.650 1.000 -0.007 -0.145

0.2 2.112 -1.603 0.198 0.956 -0.422 1.293 -1.550 0.999 -0.028 -0.259

0.3 1.952 -1.578 0.291 0.906 -0.586 1.143 -1.450 0.994 -0.058 -0.343

0.4 1.796 -1.545 0.379 0.840 -0.718 1.003 -1.351 0.987 -0.095 -0.401

0.5 1.644 -1.503 0.459 0.764 -0.822 0.873 -1.253 0.976 -0.137 -0.436

0.6 1.496 -1.454 0.532 0.677 -0.897 0.752 -1.156 0.960 -0.181 -0.451

0.7 1.353 -1.397 0.595 0.585 -0.947 0.642 -1.061 0.939 -0.226 -0.449

0.8 1.216 -1.335 0.649 0.489 -0.973 0.540 -0.968 0.914 -0.270 -0.432

0.9 1.086 -1.268 0.693 0.392 -0.977 0.448 -0.878 0.885 -0.312 -0.403

1.0 0.962 -1.197 0.727 0.295 -0.962 0.364 -0.792 0.852 -0.350 -0.364

1.2 0.738 -1.047 0.767 0.109 -0.885 0.223 -0.629 0.775 -0.414 -0.268

1.4 0.544 -0.893 0.772 -0.056 -0.761 0.112 -0.482 0.688 -0.456 -0.157

1.6 0.381 -0.741 0.746 -0.193 -0.609 0.029 -0.354 0.594 -0.477 -0.047

1.8 0.247 -0.596 0.696 -0.298 -0.445 -0.030 -0.245 0.498 -0.476 0.054

2.0 0.142 -0.464 0.628 -0.371 -0.283 -0.070 -0.155 0.404 -0.456 0.140

15

3.0 -0.075 -0.040 0.225 -0.349 0.226 -0.089 0.057 0.059 -0.213 0.268

4.0 -0.050 0.052 0.000 -0.106 0.201 -0.028 0.049 -0.042 0.017 0.112

5.0 -0.009 0.025 -0.033 0.015 0.046 0.000 -0.011 -0.026 0.029 -0.002

For cohesive soils

𝑦𝑧 = 𝐴′𝑥

𝑃𝑅3

𝐸𝑝𝐼𝑝+ 𝐵′𝑥

𝑀𝑅2


𝑀𝑧 = 𝐴′𝑚𝑃𝑅 + 𝐵′𝑚𝑀 (28) where, 𝐴′𝑦, 𝐵′𝑦, 𝐴′𝑚, 𝐵′𝑚 are coefficients (see the following figure)

𝑅 = √𝐸𝑝𝐼𝑝

𝑘

4

𝑘, see equation (9)

Fig. 5. Coefficients for long piles in cohesive soils. Adapted from (Das 2002).

2.2.7 P-Y CURVES

This method is based on results of pile lateral load tests instrumented with strain gauges along its

depth for different specific soil conditions and pile geometries.

The relationship between applied lateral load and deflection along pile’s depths can be obtained by

two steps integrations of the moment curves recorded by strain gauges and the settle of points of

control at ground line where lateral load, pile’s deflection and its slope are well known.

16

Some of the first researchers that defined the p-y curves concept were (McClelland and Focht 1958);

after them, numerous studies were done to evaluate the lateral behavior of several kind of piles

under different subsoil conditions. Even though all that information was available, there was not a

clear procedure to analyze the lateral behavior of piles laterally loaded under specific soil conditions,

that’s why, all that information was gathered and analyzed by several authors i.e. (Matlock 1970),

(Welch and Reese 1972), (Reese et al. 1974), (Reese and Welch 1975), (Murchinson 1983), and

others. They developed step by step methodologies to simulate P-Y curves for specific conditions.

These detailed procedures are used by commercial software e.g. LPile, PileLAT 2014, PyPile, ALLPILE

and others; detailed information can be found on (Reese et al. 2002) or in software’s technical

manuals.

2.2.8 CHARACTERISTIC LOAD METHOD

As a practical approach, (Duncan et al. 1994) proposed the Characteristic Load Method which is a

simplification of P-Y curves results, which is based on pile’s geometry, pile’s head restrictions, pile’s

material properties; and soil’s resistance.

Using dimensionless axes charts, lateral deflection and bending moments can be assessed as a

function of characteristic load (Pc) and the characteristic moment (Mc).

Based on (Duncan et al. 1994) the charts are suitable to be used as a hand computation; however,

this method is limited to piles and drilled shafts piles, and should not be used to estimate the lateral

behavior of deep foundations in stiff clay subjected to cyclic loadings.

2.2.9 COMPUTATIONAL MODELS

Before the improvement and the accessibility to computational tools, the analysis and design of

engineering problems were based almost exclusively on empirical considerations or restricted to

solutions of simplified mathematical equations as it is mentioned by (Desai and Zaman 2013).

Nevertheless, these simplified methodologies were not able to consider complex geometrics, load

cases, or further conditions.

17

Thanks to the advances on computational methods, many additional variants can be considered to

evaluate their significance into an engineering problem. This particularity reveals the advantages of

computational models to be used as a tool to evaluate what if scenarios.

The user of a computational tool must consider the mathematical restrictions and implications

involved in the use of a software of Finite Elements or Finite Differences, or a Plain Strain Model,

Axisymmetric Model or a 3D Model.

Even when the computational knowledge is required, if the final user concerning is about a

geotechnical simulation, he also may understand the hypothesis, advantages, limitations and how

the get the parameter of the constitutive soil model available.

According to (Brinkgreve 2005) the most commonly used geotechnical models for practical purposes

are Hooke’s law (LE), the Mohr-Coulomb model (MC), the Drucker-Prager model (DP), the Duncan-

Chang model or Hyperbolic model (DC), the Cam-Clay model (CC), the Soft Soil (Creep) model (SS(c))

and the Hardening Soil model (HS).

As it is mentioned by (Brinkgreve 2005), these models have the advantage that can be easily

implemented with a discrete geotechnical parametric characterization. In some cases, they can

even be inferred based on correlations or just estimated according to experience. The estimation

methodologies to get the parameters needed for models presented are summarize on the following

table.

18

Table 8. Overview of model parameters and selection methods. Adapted from (Brinkgreve 2005).

Par

ame

ters

Mo

de

ls

Oe

do

me

ter

CR

S

CD

CU

UU

DSS

Torv

ane

SPT

CP

T

PM

DM

T

Van

e t

est

Cla

ssif

icat

ion

Tab

les,

ru

les

C’ MC, DP, DC, SS(C), HS

D D D C C

Φ’ MC, DC, SS(C), HS

D D D C C

M (friction)

DP, CC I I I I I

Su MC, DP, DC, HS D D C C D C C

Ψ MC, HS D C

E LE, MC, DP I I I I I I C C C C C

E50ref DC, HS I C D I D I I I C C

Eurref DC, HS (D) (D) (I) (D) I C

Eoedref HS D D I I I I C C C

λ (*) CC, SS(C) D I C I I C C

K (*) CC, SS(C) (D) I C I C

μ * SSC (D) D C

V LE, MC, DP, DC I D C

Vur CC, SS(C), HS (I) C

m (power)

DC, HS D I D D C C

Konc SS(C), HS (D) C C

Rf DC, HS C

where, D means directly, (D) means directly and recalculation is needed, I means indirectly, (I) means indirectly and recalculation is needed, and C means correlation.

The parameters for most of the constitutive soil models mentioned on the previous table can also

be obtained from triaxial tests. These tests may be performed and instrumented in coherence with

the characteristics that are going to be evaluated.

To understand each of the hypothesis, restrictions, advantages and the soil parameters needed for

each soil constitutive model, it is necessary to refer to their original publications. i.e. for the

Hardening Soil Model, (Schanz et al. 1999) mention that the basis idea of the model is the hyperbolic

relationship between the deviatoric stress and the vertical strain from the primary triaxial loading.

When this happens, soil presents a decreasing stiffness before the plastic strain occurs. This

relationship, allows this model to represent in a more reliable way, the behavior of loose sands and

normally consolidated clays during a drained triaxial test.

19

The model failure criterion is the Mohr-Coulomb, then, its strength parameters are needed (φ’ and

C’). As the model has a hyperbolic relationship, a failure ratio (Rf) must be defined.

For the primary loading, the confining stress dependent secant stiffness modulus for primary loading

(E50) is needed. To relate it to different stress values, this modulus is a function of a stress referenced

modulus (E50ref), normally referenced to a 100 kPa stress (pref). In addition to this, a power coefficient

is used (m) to consider its stress dependency as a logarithmic function. The m value will depend of

the level of stress used and the material.

The same function is applied for the unloading and reloading stress paths, but, the modulus that

ought to be applied for this stress paths (Eurref) is the Young’s modulus; therefore, the unloading and

reloading stress path is elastic. Due to it, the Hooke’s law must be satisfied, and the elastic strains

computed using the Poisson’s ratio for the unloading and reloading (νur) strain estimation.

The plastic potential function adopted for the flow rule involves the use of the dilatancy angle (Ψ).

On the other hand, the plastic strain originated from the yield cap is controlled by the tangent

stiffness modulus for primary oedometer loading (Eoedref) and the coefficient of earth pressure at-

rest for normally consolidated conditions (K0NC).

2.3 MICROPILES LATERALLY LOADED

After the results of eight lateral tests reported by (Plumelle and Raynaud 1996), the concern about

the small lateral capacity of micropiles has become a constant. For that reason, the analysis of

micropile laterally tested literature has increased.

Ten lateral load tests were conducted by (Long et al. 2004) to compare the behavior predicted using

P-Y curves computed by LPILE software and the measures recorded on laterally loaded micropile

field tests. As a result, he concluded that predicted and measured was in reasonably good

agreement and that differences between measured and predicted was about ±10 percent.

(Richards and Rothbauer 2004) performed twenty lateral load tests on eight different project places

and compared their results with LPILE, NAVFAC and Characteristic Load Method estimations. The

20

results of those tests exposed that deflections can be overestimated by these methods, but they

correspond to a conservative approach.

In both works, these authors agree with the importance of a good parameter identification of the

upper 5 m and highlight the influence of the flexural stiffness in the behavior of the laterally loaded

micropile.

In North Carolina, (Babalola 2011) installed sixteen micropiles which were prescribed on a depth of

rock to perform nine single lateral load tests and a micropile group load test. He compared his

results with the P-Y curves generated by FB-MultiPier software and analyzed the sensitivity of input

parameters used.

Different types of vertical and lateral tests were performed by (Abd El-aziz 2012) on hollow bar

micropiles built on a superficial thick layer of overconsolidated clayey silt to silty clay soil, overlying

a compact sand deposit; within those tests, two monotonic lateral load tests were performed to

compare them to predicted behavior by mean of P-Y curves computed by LPILE. Thus, the research

concluded that some adjustments are needed on the parameters used to compute the P-Y curve to

represent the measurements. These adjustments involved the use of parameter values not even

reported on the original formulation of P-Y curves for the type of soil of the site of study.

As an extension of (Abd El-aziz 2012) works, (Osama F. 2013) resolved to conduct eight lateral tests

on micropiles built on cohesive soils to compare his results with LPILE estimated behavior. He built

two of the eight micropiles using 18 cm of diameter and the other six with 23 cm of diameter. As

result of his research, P-Y curves fitted better for the highest diameter micropile.

(Kershaw and Luna 2014) analyzed the effect of vertical loads on the performance of lateral load

tests of single micropiles installed at a clay and shale site. According to their results, the vertical

load has a minimal effect on the lateral behavior of micropiles installed in stiff clay.

(Rabab’ah et al. 2014) used a 2D Finite Element Analysis to evaluate the effect of micropiles

installation in the performance of an existing bridge abutment wall and its foundations, previous to

its renovation. Based on lateral evaluations using LPILE and a plain strain model using a commercial

21

2D finite element (FE) software and a Mohr Coulomb Model, they concluded that P-Y curves

overestimate the lateral displacement and that a good agreement can be obtained using a FE model.

22

3 CASE STUDY

3.1 DESCRIPTION

The case study is in Sabaneta, Colombia; close to Sabaneta’s downtown as it is presented in Fig. 6

(see project’s pin). The project is a residential complex of 10 buildings with 28-stories, vertical

service loads at foundation level between 6.7 and 15.6 MN and lateral seismic loads of 6 MN per

support. Both loads were obtained using the NSR-10 guideline.

Fig. 6. Project location. After Google Earth 2016.

This research focuses on the evaluation of methodologies frequently used in geotechnical practice

to analyze the lateral behavior of micropiles and their reliability to reproduce measurements

obtained from a lateral load test performed on an IRS micropile regularly used in Aburrá Valley.

23

3.2 GEOLOGICAL CHARACTERISTICS

According to (Área Metropolitana del Valle de Aburrá 2007), the geological units that surround the

project site are soils derived from rocks that belong to Grupo El Retiro in the Complejo Cajamarca,

which is composed by Esquistos de Cajamarca (TReC) and Migmatitas de Puente Peláez (TTmPP).

At the same time, there are different types of soil deposits: alluvial (Qal or Qat) and mudflow with

debris (NQFll), and in some places, are anthropic fills (Qll). This is illustrated on Fig. 7.

Fig. 7. Regional geology. After (A.M.V.A 2007).

3.2.1 MIGMATITAS DE PUENTE PELÁEZ (TRMPP)

This geological unit corresponds to soils derivate from migmatite rocks, which are characterized by

their compositional banding and shales. These rocks are principally constituted by quartz, feldspar

and micas, they have a migmatite structure which presents several white and white-yellow bands,

due to leucosome’s present, and dark grey bands by melanosome.

24

3.2.2 DEPÓSITOS DE FLUJO DE LODOS Y/O ESCOMBROS (NQFII)

Corresponds to soils deposited with variable thickness (around two meters) which are mud-flows

mud-supported with sub-angular boulders of gneiss, shales and quartz.

3.3 GEOTECHNICAL CHARACTERISTICS

To identify the geotechnical characteristics of the underlaying soil, a geotechnical survey program

had been done for 5 of the 10 buildings projected. The survey involved 28 (22 in the original site

conditions and 6 posteriors to excavations) Standard Penetration Tests (SPT), 6 Down Holes (DH)

and 8 geophysical linear arrays of seismic analysis of surface wave (SASW) methods (1 of theses was

performed after micropiles construction and beside them). These field tests were located as shown

in Fig. 8.

Fig. 8. Geotechnical survey location on the original terrain conditions.

25

Based on field test results, visual inspection of samples and some laboratory test results, it was

possible to identify the geotechnical characteristics of each of the materials that constitute the soil

profile.

Each sample obtained from SPT was visually described and some of them were chosen for laboratory

tests. Disturbed samples were used to make a basic geotechnical characterization based on water

contents, density, specific gravity, the Unified Soil Classification System (USCS), and gravimetric and

volumetric relationships. On the other hand, undisturbed samples were selected to determine their

undrained and drained soil resistance parameters using unconfined compression tests, consolidated

drained direct shear tests and consolidated undrained compressional triaxial test with pore pressure

record.

3.3.1 SURVEY RESULTS

Micropiles vertically (M-PC-V) and horizontally tested (M1-PC-H and M2-PC-H) were located as it is

shown in Fig. 9. It is also shown in this figure, the location of the closest field tests which are: SPT

14’088-T01, SPT 13’101-T02, SPT Integral 01 and DH Integral 01; and 3 geophysical linear arrays (the

dashed one was performed after micropiles construction).

26

Fig. 9. Location of field tests and micropiles vertically and horizontally tested.

Even though not all the triaxial tests were done on the field tests shown in the previous figure, they

were made on the same material. These laboratory tests will be used in the following chapters,

then a brief discussion will take place there.

Fig. 10 summarizes the results of index laboratory tests including classification based on the USCS,

content of fines, void ratio, dry and total densities and water content. Fig. 11 supplements the index

laboratory tests with the soil resistance parameters obtained from laboratory tests, field exploration

program results (shear wave velocities previous to micropiles construction - vs-P- and after

micropiles construction - vs-A, and SPT blow counts) and the adopted soil profile.

Fig. 12 presents the SPT blow counts corrected by energy, sampler diameter, sampling method and

overburden pressure to get the (N60) values, (Kishida 1967) correlation applied to get the effective

friction angle (φ’) and compared it with consolidated direct shear tests (DST) results. Also, there is

the Es evaluated using N60 and shear wave velocities (vs) values according to (GCO 2006) and (Mayne

2006) formulations respectively.

Fig. 10. Summary of basic characterization laboratory tests.

28

Fig. 11. Summary of field tests and mechanical soil resistance based on some laboratory tests.

29

Fig. 12. Summary of soil parameters.

The most superficial layer of the simplified geotechnical profile corresponds to man-made fills

conformed during the construction of existing buildings that were located on project site. This layer,

was entirely removed during construction of current project execution, therefore it will not be

further discussed.

NQfll layer is a heterogeneous material with boulders as those shown on Fig. 13 and a soil matrix

classified as silty sands and silty clays as is illustrated on Fig. 10.

Fig. 13. NQfll's boulder.

Under this layer, a residual soil profile is easily identified by its characteristic texture derived from

parental rock, the reduction of soil’s water content, the increase of soil’s resistance directly

associated with the SPT blow count, and the decrease of void ratio and the rise of soil’s density. If

this soil profile is associated to (Fookes 1997) residual’s soil description, it is quite simple to relate

each soil layer to specifics horizons. In this survey, three differentiable soil layers were found

under NQfll layer, these ones were classified as part of the horizons V and IV. In the following

figure, the first two materials which are below NQfll layer are presented.

31

Fig. 14. Res. V and Res. V (2) materials.

In the following table, a summary of the index and the resistance Mohr coulomb’s soil parameters

for each layer is presented.

Table 9. Basic Index and soil’s resistance parameters.

Layer e W (%) γ (kN/m3) Su (kPa) C’ (kPa) Φ’ (°) Es (kPa)

Min (m) Max (M) m M m M m M m M m M m M

NQfll 0.9 1.4 18 50 16 19 34 128 11 27 20 38 3 35

Res. V 1.0 1.6 42 58 16 18 48 99 4 53 20 29 4 52

Res. V (2) 0.7 1.3 32 54 17 19 39 41 30 34 23 31 12 55

Res. IV 0.6 0.6 14 41 20 20 - - 0 0 24 41 19 82

32

3.4 MICROPILES LOAD TESTS

As it was mentioned previously, three load tests were performed at project site, those were

performed following the guidelines of as per ASTM D 1143 and ASTM D 3966. The results of these

tests are presented and briefly discussed on next paragraphs; but it is important to mention that:

• 4 m were cut before tests were carried out, then fills layer were removed.

• Micropiles were 27 m length and their initial diameter was 20 cm.

• Micropiles classified as Type D (FHWA 2005).

• Micropiles were built using an IRS method, and pressure varied between 700 to 1100 kPa,

increasing at depth.

• Longitudinal micropiles’ reinforcement was 4 #10 steel bars.

• Transversal micropiles’ reinforcement used steel stirrups each 0.15 m.

• Final average micropiles’ diameter after injection varied between 30 and 35 cm, in

correspondence with construction registers and exhumated measurements.

Some illustrative pictures of site conditions and micropiles built are presented on next figures.

33

Fig. 15. Site conditions and micropile's reinforcement.

34

Fig. 16. Exhumed micropiles.

35

3.4.1 VERTICAL LOAD TEST

The test was performed according to ASTM D 1143 guidelines, this test consisted of a hydraulic jack,

7 extensometers (5 in the central micropile and 1 in each of the reaction micropiles) and three

micropiles: two reaction micropiles, set at the sides and one central, where the hydraulic jack is

located. Test arrangement and its results can be seen in the following figure.

Fig. 17. Vertical load test - M-PC-V.

The curve shown above illustrates that the micropile behaved approximately linearly until 1570 kN

load, where 17 mm vertical displacement were measured, after that, the slope of this curve

changed and deformations enlarged without any significant increment of load.

Considering that reinforcement bars were 4 #10 conventional steel bars, it is expected that

yielding point load be reached at 350 kN per bar, so, for the 4 steel bars the total yielding point

load could be 1400 kN, based on that, it is considered that soil did not fail and reinforcement did.

0

200

400

600

800

1000

1200

1400

1600

1800

0 5 10 15 20 25

Load

(kN

)

Displacement (mm)

36

3.4.2 LATERAL LOAD TEST

After three months that vertical load test ended, the reaction micropiles were used for the lateral

load tests.

The lateral load test procedure was designed to fulfill the ASTM D3966-07 requirements. The basic

concept of this test is to set a reaction support, then, apply a lateral load using a hydraulic jack

between the reaction and the micropile tested, finally, record each lateral displacement in the

reaction and the micropile and the load applied. The features of each of the elements used during

tests were:

- Reactions: a concrete deadman of 0.6 m width, 0.6 m length and 0.5 m depth.

- Hydraulic Jack: Enerpac RCH-202.

- A hydraulic hand pump.

- A pressure gauge.

- Two bearing plates.

- Electronic displacement indicators: two Mitutoyo ABSOLUTE Digimatic Indicator ID-U SERIES

575-123.

- A reference beam.

- Two wirelines, four mirrors and two scales.

The arrangement and the results of the tests are presented on the following pictures.

37

a b

Fig. 18. Lateral Load tests. a) M1-PC-H and b) M2-PC-H results.

The analyses of the behavior of the micropile laterally loaded is the purpose of the following chapter.

However, it is important to notice the difference between both results. This is due to the micropiles

proximity to the slopes of the road as can be inferred from Fig. 9. M1-PC-H is 7 m to the crest of the

slope, while M2-PC-H is just 2.4 m to 4.4 m to the crest of the slope which inclination varies from

18° to 40° respectively.

0

20

40

60

80

100

0 10 20 30

Load

(kN

)

Displacement (mm)

0

20

40

60

80

100

0 10 20 30 40 50

Load

(kN

)

Displacement (mm)

38

4 ANALYSES

4.1 CURRENT PRACTICAL USED MODELS

In structural practice engineering it is common to model soil as springs (modulus of subgrade

reaction) and foundation elements like beams. These springs are considered linear perfectly elastic

and are commonly used for all stages and load combinations as a constant without considering soils

spatial variation, its resistance degradation due to cyclic load, the effect of construction techniques,

special boundary conditions and soils variation of stiffness for the stress changes during

construction and operation process.

From this point of view, geotechnical engineers must define which springs should be used for

structural analysis, considering all previous mentioned variables.

For practical engineering purposes, it is common to use semiempirical formulations or P-Y curves

limited to a specific lateral deformation at foundation element’s upper part, to define these springs.

It is important to notice that semiempirical formulations or P-Y curves have their own limitations

and cannot be used for all conditions. For example, P-Y curves were developed for large piles and

not for smaller once as it is mentioned by (Reese et al. 2002), as a consequence, it is possible to get

a good approach to piles’ internal solicitations, but if the lateral displacements are the concern, it

will not be a consistent method.

A lateral load test is rarely performed to check theoretical spring values used and ultimate lateral

displacement, for this reason, it is important to evaluate the reliability of methods commonly used

in practical engineering and try to recreate the measurements obtained from large scale tests.

4.2 MODELING

In the following paragraphs, the evaluation of micropile M1-PC-H will be presented using

semiempirical methods, P-Y curves and computational geotechnical modelling.

39

4.2.1 BEAM ON ELASTIC FOUNDATION USING SEMIEMPIRICAL FORMULATIONS

To evaluate the lateral behavior of micropile M1-PC-H, the range of parameters presented in Fig. 10

to Fig. 12, and Table 9 were applied to equations (9) to (20), and were assigned to an elastic beam

element.

Table 10 to Table 12 present the moduli of subgrade reaction computed for the lowest, the average

and the highest NQfll soil’s parameters respectively. The remainder subgrade reaction moduli

evaluation can be consulted on annexes Annex 1 to Annex 6.

Table 10. NQfll layer moduli of subgrade reaction - semiempirical formulations - Lowest case.

Formulation kh (kPa/m) Parameters

(Vesic 1961) 4391 Es=3 MPa, v=0.3, d=0.3 m, Ip=3.97E-4 m4, Ep=33GPa

(Francis 1964) 1184060 Z=3m, γ=16kN/m3, φ=20°, Ny=2.9, Nq=6.4, d=0.3m

(Broms 1964a) 3131 Es=3 MPa, v=0.3, d=0.3 m, L=27 m, m=0.37


100987 Z=3m, γ=16kN/m3, φ=20°, Nq=6.4, yu=6mm, y=2.54mm


8781 Es=3 MPa, v=0.3, d=0.3 m, Ip=3.97E-4 m4, Ep=33GPa

(Robinson 1979)

7593 Su=34kPa, d=0.3m


69109 N=2, d=0.3m, Y=2.54mm

(Sogge 1981) 3142 Z=3m, d=0.3m


20000 Es=3 MPa, d=0.3 m


154248 Z=3m, σ’=48kPa, γ=16kN/m3, φ=20°, A=5, d=0.3m, y=2.54mm

Table 11. NQfll layer moduli of subgrade reaction - semiempirical formulations - Intermediate case.


(Vesic 1961) 19003 Es=12MPa, v=0.3, d=0.3 m, Ip=3.97E-4 m4, Ep=33GPa

(Francis 1964) 10849512 Z=3m, γ=19.5kN/m3, φ=37.6°, Ny=59.2, Nq=46.2, d=0.3m

(Broms 1964a) 12523 Es=12MPa, v=0.3, d=0.3 m, L=27 m, m=0.37


889204 Z=3m, γ=19.5kN/m3, φ=37.6°, Nq=46.2, yu=6mm, y=2.54mm


38005 Es=12MPa, v=0.3, d=0.3 m, Ip=3.97E-4 m4, Ep=33GPa

(Robinson 1979)

4556 Su=20.4kPa, d=0.3m

40


172772 N=5, d=0.3m, Y=2.54mm

(Sogge 1981) 3142 Z=3m, d=0.3m


80000 Es=12MPa, d=0.3 m


187989 Z=3m, σ’=58.5kPa, γ=19.5kN/m3, φ=37.6°, A=5, d=0.3m, y=2.54mm

Table 12. NQfll layer moduli of subgrade reaction - semiempirical formulations - Highest case.






916986 Z=3m, γ=19kN/m3, φ=38°, Nq=48.9, yu=6mm, y=2.54mm


121191 Es=35 MPa, v=0.3, d=0.3 m, Ip=3.97E-4 m4, Ep=33GPa

(Robinson 1979)

28587 Su=128kPa, d=0.3m


1382176 N=40, d=0.3m, Y=2.54mm

(Sogge 1981) 3142 Z=3m, d=0.3m


233333 Es=35MPa, d=0.3 m


183169 Z=3m, σ’=57kPa, γ=19kN/m3, φ=38°, A=5, d=0.3m, y=2.54mm

It is worth noting that for these evaluations, pile’s modulus of elasticity was computed using the

equivalent modulus of the composed micropile section (33 GPa), the bearing capacity factors were

calculated using (Meyerhof 1963) formulation, the ultimate lateral deflection was assumed as 6 mm

and admissible lateral deflection was considered as 2.54 mm.

SAP 2000 models use the beam elastic foundation principle, so, equivalent springs are necessary to

evaluate lateral displacement and internal solicitations. The moduli of subgrade reaction presented

in previous tables were multiplicated by their afferent area to convert it into an equivalent spring.

In the following figure, the SAP 2000 model used is introduced.

41

a

b

Fig. 19. SAP 2000 model. a) Micropile cross section, and b) 3D model.

The results of the lateral evaluation using the equivalent springs obtained from the semiempirical

formulations and the model presented in Fig. 19 are shown in the following group of figures, where

42

computed lateral deflection is directly compared with lateral load test measured deflection at

micropile’s head.

a

b

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50

Load

(kN

)

Displacement (mm)

Vesic (1961b)

Francis (1964)

Broms (1964)

Audibert and Nyman (1977)

Kishida and Nakai (1977)

Robinson (1979)

Bhushan et al. (1981)

Sogge (1981)

Pyke and Beikae (1984)

Habibagahi and Langer (1984)

Lateral Load Test

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50

Load

(kN

)

Displacement (mm)

Vesic (1961b)

Francis (1964)

Broms (1964)



Robinson (1979)


Sogge (1981)



Lateral Load Test

43

c

Fig. 20. Comparison between lateral load test result against lateral response of a beam on elastic foundation using

semiempirical methodologies for: a) the lowest soil’s parameters, b) average soil’s parameters, and c) the highest soil’s parameters.

Based on direct comparison of the predicted displacements and measured once, it is evident that

the predicted lateral displacement using semiempirical models fits relatively well in some cases,

nevertheless, it is not reliable, because it depends too much on the soil parameters used which will

depend in some cases on the designers’ experience, reliability and wisdom.

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50

Load

(kN

)

Displacement (mm)

Vesic (1961b)

Francis (1964)

Broms (1964)



Robinson (1979)


Sogge (1981)



Lateral Load Test

44

4.2.2 P-Y CURVES

To evaluate the lateral displacement of the micropile’s head M1-PC-H using P-Y curves method, the

software ALLPILE was implemented. In the following figure, the micropile characteristics and soils

parameters used are shown.

a

b

c

d

Fig. 21. ALLPILE Model. a) micropile characteristics, b) the lowest soil’s parameters, c) average soil’s parameters, and d)

the highest soil’s parameters.

In accordance with soil conditions presented on Fig. 21, the P-Y curves obtained at the middle of

each soil layer are presented on the following figures.

a

0

200

400

600

800

1000

1200

0 0.01 0.02 0.03 0.04

P (

kN/m

)

Y (m)

3 m

11 m

19 m

24.5 m

45

b

c

Fig. 22. P-Y curves for: a) the lowest soil’s parameters, b) average soil’s parameters, and c) the highest soil’s parameters.

Based on the elastic foundation principles and the equivalent spring for non-linear conditions; P-Y

curves previously shown, are used to compute lateral displacements of the micropile of study. In

the next group of figures, lateral load test result is directly compared against the lateral

displacement calculated for each of the scenarios previously introduced for semiempirical

evaluation. Detailed information of these evaluations can be consulted on annexes Annex 7 to

Annex 9.

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

0 0.01 0.02 0.03 0.04

P (

kN/m

)

Y (m)

3 m

11 m

19 m

24.5 m

0

2000

4000

6000

8000

10000

12000

0 0.01 0.02 0.03 0.04

P (

kN/m

)

Y (m)

3 m

11 m

19 m

24.5 m

46

a

b

0

10

20

30

40

50

60

70

80

90

100

0 50 100 150

Load

(kN

)

Displacement (mm)

Lateral Load Test

Model

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20 25 30

Load

(kN

)

Displacement (mm)

Lateral Load Test

Model

47

c

Fig. 23. Comparison between lateral load test result against lateral response of a beam on elastic foundation using P-Y curves method for: a) the lowest soil’s parameters, b) average soil’s parameters, and c) the highest soil’s parameters.

According to results, it is evident that P-Y curves can be used, nevertheless, the micropile lateral

displacement estimation can be overpredicted regardless which soil parameters are used (even if

the highest ones are applied), which means a conservative approach for displacement evaluations

as it was pointed out by (Long et al. 2004; Rabab’ah et al. 2014; Richards and Rothbauer 2004).

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20 25 30

Load

(kN

)

Displacement (mm)

Lateral Load Test

Model

48

4.2.3 COMPUTATIONAL MODEL

In the following paragraphs, a brief discussion of the soil constitutive models that must be used is

presented. After that, analyses are performed and discussed.

4.2.3.1 CONSTITUTIVE MODELS EVALUATION

To define which constitutive soil model ought to be used, some of the models presented on Table 8

were evaluated using the SoilTest module of the software MIDAS GTS NX version 2.1. Results

obtained from simulation were confronted against stress-strain tri-axial test results for the three

upper soil layers, the evaluation for the NQfll layer is presented in the following figures, the other

ones can be found on annexes.

a

0

50

100

150

200

250

300

350

400

0% 2% 4% 6% 8%

s'1

-s'3

(kP

a)

Axial strain (%)

A sample, σ3 = 25 kPa

B sample, σ3 = 50 kPa

C sample, σ3 = 100 kPa

Model - A sample

Model - B sample

Model- C sample

49

b

c

Fig. 24. NQfll constitutive model evaluation. a) Mohr Coulomb model, b) Duncan-Chang model and c) Hardening Soil

model.

0

50

100

150

200

250

300

350

400

0% 2% 4% 6% 8%

s'1

-s'3

(kP

a)

Axial strain (%)




Model - A sample

Model - B sample

Model- C sample

0

50

100

150

200

250

300

350

400

0% 2% 4% 6% 8%

s'1

-s'3

(kP

a)

Axial strain (%)




Model - A sample

Model - B sample

Model- C sample

50

According to Fig. 24, the best model to represent the soil test behavior is the Hardening Soil Model.

Considering this, it will be used to simulate the soil behavior of the three upper layers, and for the

bottom one, a Mohr Coulomb model will be employed.

The model and the parameters used to represent each soil layer are summarized in the following

tables.

Table 13. Constitutive soil parameters for each soil layer modeled with HS.

Parameter NQfll Res. V Res. V (2)

γ (kN/m3) 19.5 17.9 19.7

γd (kN/m3) 15 12.8 15.6

ν 0.35 0.35 0.35

C’ (kPa) 11.50 - -

Φ’ (°) 37.57 - -

C (kPa) - 52.5 30

Φ (°) - 16 16

Ψ (°) - - -

E50ref (kPa) 20700 5770 4230

Eoedref (kPa) 20700 5770 4230

Eurref (kPa) 62100 17310 12690

Pref (kPa) 100 100 100

m (power) 1 1 1

Konc 0.39 0.72 0.72

Rf 0.9 0.9 0.9

Table 14. Constitutive soil parameters for each soil layer modeled with MC.

Parameter Res. IV

γ (kN/m3) 20

γd (kN/m3) 17

ν 0.3

C’ (kPa) 0

Φ’ (°) 35

Ψ (°) -

E (kPa) 82000

4.2.3.2 LATERAL BEHAVIOR

After calibration of the HS model for the three first layers and the assumption of the MC model for

the bottom one, the 3D model was settled as is shown in the following figure.

51

a

b

Fig. 25. 3D model. a) soil layer and b) micropile element.

Soil parameters used for each soil layer were established on Table 13 and Table 14. First layer (NQfll)

thickness is 6 m, second one (Res. V) is 10 m, the third one (Res. IV(2)) is 6 m and the last one (Res.

IV) is 20 m. Phreatic level position is 12 m below top layer surface. The micropile element is

considered as a beam element directly connected to each soil layer mesh (without using interfaces).

Micropile properties are presented on the following figure.

a

b

Fig. 26. Micropile characteristics. a) equivalent material properties and b) cross section.

52

It is important to notice that the equivalent resistance was used to consider the composite section

of micropile element as it was done on previous evaluations.

The dimensions of the model were 10 m wide, 10 m long and 42 m high. The meshing elements

used were rectangular finite elements the size of 1 m. The boundary conditions at the lateral sides

corresponded to horizontal translational constraints and in the bottom of the model a vertical

displacement constraint. The micropile element was restricted to rotation on its vertical axis.

For the lateral evaluations of the micropile this was laterally loaded by means of a point load placed

at its head. This load was increased by stages. For these evaluations, three scenarios were

considered:

• First one: soil parameters of Table 13 and Table 14 are used.

• Second one: moduli of elasticity and Over Consolidation Ratio (OCR) are scaled.

• Third one: a Mohr Coulomb model is used and moduli of elasticity are determined based on

(Mayne 2006) methodology and post micropile construction Vs measurements shown in Fig.

11 as Vs-A.

For these scenarios, the geometry of the model and the micropile are kept as a constant, and just

soil properties are changed.

4.2.3.2.1 Initial conditions (1s scenario)

Using directly the calibrated soil models to evaluate the lateral behavior of a micropile type IV will

get results like those presented on the following figure.

53

a

b

Fig. 27. Lateral displacement evaluation at: a) micropile's head and b) along micropile's depth.

It is important to notice that the model did not converged because the soil resistance was too low,

nevertheless, from the previous figure is quite notable that at 6 m depth is presented a slope change

in the micropile deformation shape, this implies an inflection point and possibly a plastic hinge. This

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50

Load

(kN

)

Displacement (mm)

Lateral Load Test

Model

0

3

6

9

12

15

18

21

24

27

30

-10 -5 0 5 10 15 20 25 30 35 40 45

De

pth

(m

)

Displacement (mm)

Initial 10 kN 20 kN 30 kN

54

result presents a good agreement with Table 15. Considering this, then, the lateral behavior of the

micropile is primarily defined by the first soil layer.

Table 15. Evaluation of equations (2) to (4).

Author Equation (FHWA 2005) 𝐿0 = 20 ∗ 0.3 m = 6 m (29) (Richards and Rothbauer 2004) 𝐿0 = 2 to 5 m (30)

(L’École Nationale des Ponts et Chaussées 2004) 𝐿0 = √

4 ∗ 33 𝐺𝑃𝑎 ∗ 3.97𝐸−4 𝑚4

20.7 𝑀𝑃𝑎

4

= 1.3 𝑚 (31)

4.2.3.2.2 Scaled stress (2d scenario)

To consider the effect of the soil improvement based on the micropile injection procedure, then,

taking account, the discussion presented on the previous section, for the first soil layer the reference

soil modulus for primary loading was scaled to the pressure of injection used at surface (1000 kPa)

and the OCR to 50 (ratio between the average insitu horizontal effective stress and the injection

pressure applied on the first layer – it is between 45 to 50).

a

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20 25 30

Load

(kN

)

Displacement (mm)

Lateral Load Test

Model

55

b

Fig. 28. Lateral displacement evaluation with NQfll’s reference modulus and OCR scaled. a) micropile's head and b) along

micropile's depth.

Results obtained from the model after considering the increased effect of soil’s stiffness and

resistance due to injection pressure used to build the micropile, show a decent agreement with

lateral load test measurements. This implies that modelling must consider the use of a soil

constitutive model that could be able to reproduce laboratory tests concerning characteristic as

good as possible, the construction techniques used and to scale stress and resistance due to soil’s

disturbances.

4.2.3.2.3 Second approach (3d scenario)

As an alternative to evaluate the lateral behavior of the micropile of interest, a Mohr Coulomb

model was used for the first soil layer (NQfll), nevertheless, the soil modulus used (E50) to consider

the effect of the injection procedure was computed with the Vs measured after the injection

procedure. The modulus used for the evaluation was the highest one for NQfll layer after some

micropiles were constructed (see Fig. 12).

0

3

6

9

12

15

18

21

24

27

30

-4 -2 0 2 4 6 8 10 12 14 16 18

De

pth

(m

)

Displacement (mm)

Initial 10 kN 20 kN 30 kN 40 kN 50 kN 60 kN 70 kN

56

a

b

Fig. 29. Lateral displacement evaluation with NQfll Mohr Coulomb model using soil’s modulus after injection. a)

micropile's head and b) along micropile's depth.

The MC model seems to be enough to consider elastic part behavior of the soil and the lateral load

test result. Nonetheless, it is just usable if complementary geotechnical surveys after micropiles

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20 25 30

Load

(kN

)

Displacement (mm)

Lateral Load Test

Model

0

3

6

9

12

15

18

21

24

27

30

-4 -2 0 2 4 6 8 10 12 14

De

pth

(m

)

Displacement (mm)

Initial 10 kN 20 kN 30 kN 40 kN 50 kN 60 kN 70 kN

57

have been entirely built is performed and if a limited lateral displacement value of 1 cm is considered

as a boundary condition.

58

5 ADDITIONAL APPROACH

Considering the increase of geophysical exploration methods used nowadays and some of their

results -shear wave velocity (Vs). It could be reasonable to expect an approach to compute the

modulus of subgrade reaction derived directly from Vs results. A brief discussion about a

proposed formulation is presented in the following paragraphs.

The shear stress (τ) is:

𝜏 = 𝐺 𝛾 (32) where, 𝐺 is the shear modulus and 𝛾 is the shear strain.

Also:

𝜏 =𝐹

𝐴

(33)

where, 𝐹 is the internal shear force and 𝐴 is the area of the section where shear force is acting.

By definition:

𝑣𝑠 = √𝐺

𝜌

2

(34)

where 𝜌 is the soil density.

Replacing 𝐺 from (34) into (32) it results into:

𝜏 = 𝑣𝑠2 𝜌 𝛾 (35)

And (33) in (35):

𝐹

𝐴= 𝑣𝑠

2 𝜌 𝛾 (36)

Based on (5):

𝑘 𝑦

𝐴= 𝑣𝑠

2 𝜌 𝛾 (37)

Then, leaving 𝑘 from (37):

𝑘 =𝑣𝑠

2 𝜌 𝛾 𝐴

𝑦

(38)

59

Fig. 30. Soil shear stress conditions during a lateral load test.

As it is inferred from Fig. 30, 𝛾 =𝑦

𝐻 and 𝐴 = 𝑀𝑖𝑐𝑟𝑜𝑝𝑖𝑙𝑒 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟 (𝑑) ∗ 1𝑚. Considering these

variables values, then:

𝑘 =𝑣𝑠

2 𝜌 𝑑 ∗ 1𝑚

𝐻

(39)

If (39) is multiplied and divided by gravity (g), then:

𝑘 =𝑣𝑠

2 𝛾 𝑑 ∗ 1𝑚

𝐻 𝑔

(40)

It is important to mention that this equation is based on elasticity theory, consequently, it can be

used just to represent soil’s elastic response. Using equation (40), the following results were

obtained to represent the elastic part of the load test.

60

Fig. 31. Evaluation of M1-PC-H lateral load test result again proposed formulation for the elastic part.

The most fitted results were obtained using the middle height of each soil layer and its

correspondent shear wave velocity. The value of 𝑘 used for each soil layer is shown in Table 16.

Table 16. Moduli of subgrade reaction using proposed formulation for springs each meter along micropile element.

Soil layer Vs (m/s) K (kN/m)

NQfll 218 7153

Res. V 239 6666

Res. V (2) 283 15490

Res. IV 298 19843

As an additional effort to evaluate the reliability of equation (40), the M2-PC-H lateral load test

result is compared with the latest results, but this time influenced by the coefficients of reduction

proposed by (Mezazigh 1995). For this evaluation, the conditions mentioned on3.4.2 are used to

obtain the reduction coefficients and the result of this is presented on Table 17.

Table 17. Evaluation of coefficients of reduction due to slope proximity using (Mezazigh 1995).

t (m) 2.4 4.4

B or D (m) 0.3

β (°) 18 40

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20 25 30

Load

(kN

)

Displacement (mm)

Lateral Load Test

Detailed Vs

Vs at the center of the soillayer

Minimun soil layer Vs

61

tlim (m) 1.14 4.84

r 1.30 0.72

t≤tlim No Yes

Based on Table 17 results, the reduction coefficient is 0.72. Then, the new moduli of subgrade

reaction are:

Table 18. Moduli of subgrade reaction using proposed formulation and (Mezazigh 1995) methodology.

Soil layer Reduction coefficient K (kN/m)

NQfll

0.727

5205

Res. V 4851

Res. V (2) 11273

Res. IV 14441

Using these new values, the displacement obtained is compared against the recorded M2-PC-H

lateral load test as is shown in the next figure.

Fig. 32. Evaluation of M2-PC-H lateral load test result compared to proposed formulation for the elastic part and affected by (Mezazigh 1995).

It is important to note that the upper 6 m of soil controls the lateral behavior of the micropile,

then, it will be necessary to perform additional instrumented tests to verify the truthfulness of this

0

10

20

30

40

50

0 5 10 15 20

Load

(kN

)

Displacement (mm)

Vs at the center of the soillayer

Lateral Load Test

62

proposed method. Tentatively, this elastic method must be restricted to micropiles lateral head

displacement not larger than 1 cm. To represent the plastic part of the micropile behavior, maybe

the use of degradation curves could be used.

A comparison between the semi-empirical methods that consider the elasticity modulus as a main

parameter and the proposed formulation can be performed if (Mayne 2006) methodology is

applied to degrade the initial shear modulus and transform it into the equivalent soil modulus as it

is pointed out by (Salvá 2014).

To do this degradation, an hyperbolic function is applied using a safety factor between 1.5 and 3

(as it is normally used for foundation systems), a 𝑔 value of 0.3 (the most feasible results are found

using 𝑔 values varying between 0.2 and 0.4), a 𝐹 value of 1 (this is suggested by (Mayne 2006))

and taking into account that the most fitted results were obtained using (40) with H equal to 3 m,

then, the proposed formulation will result in the following equation.

𝑘 = 3.3 ∗𝐸𝑠 ∗ 𝑑

(1 + 𝑣) 𝑡𝑜 1.3 ∗

𝐸𝑠 ∗ 𝑑

(1 + 𝑣)

(41)

This new equation could be compared with those presented on Table 3, and easily identify that it

is similar to (Vesic 1961), (Kishida and Nakai 1977) and (Broms 1964a), nevertheless, this proposal

could be used from direct measurements of the shear wave velocity, what means an advantage

because it reduces subjectivity.

63

6 CONCLUSIONS AND RECOMMENDATIONS

Based on results shown on previous chapters, the following conclusions and recommendations are

drawn from the evaluation of lateral response of a micropile type IV (IRS) laterally loaded.

6.1 CONCLUSIONS

1. As references and for practical engineering approaches, the ultimate lateral load of a

micropile can be considered at least as 4% of the ultimate vertical load.

2. The use of semiempirical formulations to evaluate lateral displacement of a micropile may

result in an over or underestimation of the lateral displacement depending of the

parameters and the formulation applied. It will be the responsibility of the geotechnical

engineer designer to evaluate which of these formulations ought to be used, based on his

professional experience and parametrical reliability.

3. Lateral displacements estimation using P-Y curves for silts will result in a conservative

approach independently of which geotechnical parameters are implemented.

4. Even though geotechnical engineers have calibrated constitutive soil models that can

accurately represent the characteristics that will be evaluated (displacements, pore

pressures, etc.), it is important to consider the effects on the stress conditions of soil

according to the construction techniques that are used. If this is not taken into account, the

lateral displacements evaluated will be overpredicted.

5. If it is not possible to calibrate advanced soil constitutive models, alternatively, a Mohr

Coulomb soil model can be used if a post-grouted injection survey can be performed with

at least a geophysical field test to evaluate the increase in the soil modulus of elasticity as

consequence of the soil’s densification effect of the injections. However, this evaluation

method will be just valid for the elastic range of the soil and reliable for lateral

displacements lower than 1 cm.

64

6.2 RECOMMENDATIONS

A. As a complementary condition of evaluation, it is necessary to compute the reduction of the

lateral resistance by the presence of slopes near the micropile. This is quite evident in the

comparison of the results of Fig. 18.

B. This research focused on the analysis of response of a single micropile, nevertheless it could

be interesting to evaluate the performance of a group of micropiles laterally loaded and the

effect of the separation between elements.

C. To supply the horizontal resistance of micropiles installed vertically, the use of battered

micropiles or anchors in the micropile group’s cap will be desirable.

D. To verify the representativeness of the numerically evaluated deformed shape, it will be

necessary to perform another test, but this time instrumented with strain gauges along its

length.

E. Considering that the main concern about lateral loads results from external sources like

earthquakes and wind forces, it will be necessary to evaluate the soil’s resistance

degradation by the effect of cyclic loads.

F. It would be highly recommended to use steel cases as reinforcement for the first 6 m of the

micropile, this will help to improve the stiffness of the element and may help to increase

lateral resistance.

66

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72

8 ANNEXES

Semiempirical evaluations

Formulation Kh (kPa/m)

Parameters




(Audibert and Nyman 1977) 370284

Z=11m, γ=16kN/m3, φ=20°, Nq=6.4, yu=6mm, y=2.54mm

(Kishida and Nakai 1977) 11560 Es=4MPa, v=0.3, d=0.3 m, Ip=3.97E-4 m4, Ep=33GPa

(Robinson 1979) 10720 Su=48kPa, d=0.3m

(Bhushan et al. 1981) 69109 N=2, d=0.3m, Y=2.54mm

(Sogge 1981) 11520 Z=11m, d=0.3m

(Pyke and Beikae 1984) 26667 Es=4MPa, d=0.3 m

(Habibagahi and Langer 1984) 722512

Z=11m, σ’=166kPa, γ=16kN/m3, φ=20°, A=5, d=0.3m, y=2.54mm

Annex 1- Res. V layer moduli of subgrade reaction - semiempirical formulations – Lowest case


Parameters









(Sogge 1981) 11520 Z=11m, d=0.3m




Annex 2. Res. V layer moduli of subgrade reaction - semiempirical formulations -Highest case.


Parameters







73



(Sogge 1981) 20945 Z=20m, d=0.3m




Annex 3. Res. V (2) layer moduli of subgrade reaction - semiempirical formulations - Lowest case.


Parameters






(Kishida and Nakai 1977) 197753 Es=55 MPa, v=0.3, d=0.3 m, Ip=3.97E-4 m4, Ep=33GPa



(Sogge 1981) 20945 Z=20m, d=0.3m




Annex 4. Res. V (2) layer moduli of subgrade reaction - semiempirical formulations - Highest case.


Parameters


(Francis 1964) 17081628 Z=23.5m, γ=20kN/m3, φ=24°, Ny=5.7, Nq=9.6, d=0.3m



Z=23.5m, γ=20kN/m3, φ=24°, Nq=9.6, yu=6mm, y=2.54mm




(Sogge 1981) 24611 Z=23.5m, d=0.3m



Z=23.5m, σ’=335kPa, γ=20kN/m3, φ=24°, A=5, d=0.3m, y=2.54mm

Annex 5. Res. IV layer moduli of subgrade reaction - semiempirical formulations - Lowest case.


Parameters


(Francis 1964) 132232692

Z=23.5m, γ=20kN/m3, φ=41°, Ny=114, Nq=73.9, d=0.3m


74


Z=23.5m, γ=20kN/m3, φ=41°, Nq=73.9, yu=6mm, y=2.54mm




(Sogge 1981) 24611 Z=23.5m, d=0.3m



Z=23.5m, σ’=335kPa, γ=20kN/m3, φ=41°, A=5, d=0.3m, y=2.54mm

Annex 6. Res. IV layer moduli of subgrade reaction - semiempirical formulations - Highest case.

P-Y curves:

77

Annex 7. Lateral evaluation using P-Y curves - lowest case.

81

Annex 8. Lateral evaluation using P-Y curves - average case.

85

Annex 9. Lateral evaluation using P-Y curves – highest case.

86

HS - model evaluation:

Annex 10. Res. V. HS Model calibration.

Annex 11. Res. V (2). HS Model calibration.

0

50

100

150

200

250

300

0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20%

s'1

-s'3

(kP

a)

Axial strain (%)

Model, sample A

Model, sample B

Sample A, σ3 = 150 kPa

Sample B, σ3 = 250 kPa

0

50

100

150

200

250

300

350

400

0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20%

s'1

-s'3

(kP

a)

Axial strain (%)

Sample A, σ3 = 150 kPa

Sample B, σ3 = 250 kPa

Sample C, σ3 = 350 kPa

Model, sample A

Model, sample B

Model, sample C

evaluation of a micropile laterally loaded using

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